No it didn't, and as our views on the manner in which these fell are similar I am going to dig my heels in here because it is worth it. I want you to picture the tower in sway - it acts as a cantilevered beam would, one side goes into compression and the other tension. The short span sides would normally act as the beam web and equalise in the centre. Given that you and I can see that the hat truss joins all of these 4 sides, we must then surely agree that in sway the net force on the hat truss is zero. You are conflating NIST's description of what the hat truss did in redistributing overstress from core to perimeter in their alleged failure mode of the towers, with the structural function of the truss. It's probably one of the most common errors to make, and it is one of the most important to correct because in understanding the true function of it, the true failure mode can be easier seen. And that was failure in the cores, that could only happen by the removal of mass below the height of impact, and this is what truly buries NIST's BS story. I'm not trying to talk down to you here, honestly.